that's what the mouse and ssh seem to have in common
.....
When logged in locally using the X server it crashes. I suspect a

measure of software involvement in the crashes, because when I upgraded
the nvidia drivers from 1.0.8756-1 to 1.0.8762-2 and also upgraded the
kernel from 2.6.12 to 2.6.15 the crashes became less frequent.

First thing to try: get rid of the closed-source nVidia drivers and try
using the i-tal "nv" driver instead. See how the system fares then.

And run your sticks of RAM, one at a time, through memtest, for a good
24 or so hour run

Well, memtest alias memtester, when asked to test all, allocated 3G of
memory -- I only have 2G on my machine, and then failed to lock all of
them into physical RAM -- small wonder. Then it got killed. Does it
have no mechanism for distinguishing whether it's testing RAM or swap
space?